In a large saucepan, combine the milk, rice and sugar with 2 cups of water and bring to a boil. Simmer over moderate heat, stirring frequently, until the rice is tender and suspended in a thick, creamy sauce, about 30 minutes. Stir in the coconut milk and simmer, stirring occasionally, until the rice is very tender and the liquid is thickened, about 10 minutes. Let cool slightly.

In a medium saucepan, toast the coconut over moderate heat, stirring constantly, until fragrant and golden, about 4 minutes. Transfer to a plate to cool.

Spoon the rice pudding into bowls, garnish with the toasted coconut and serve.